High resolution photon emission computed tomographic imaging tool

ABSTRACT

An brain scanning apparatus having a scanner device and a host computer. The scanner radiation detectors detect radiation emitted from a desired portion, or slice, of a brain source. The scanner device contains microprocessors and code which control the movement of the radiation detectors and performs the data acquisition over a number of slices and transmits this data to the host computer. The host computer initiates a scan by sending desired setup parameters to the scanner device and instructing the scanner to begin collecting data. During the scan, acquired data is sent to the host computer and spooled to a hard disk. The computer can be instructed to perform a slice by slice reconstruction of the source brain while the scan is taking place in order to produce a 2-dimensional reconstruction of the mapped brain. A complete 3-dimensional reconstruction of all the compiled slices is performed and visually displayed after acquisition of all the required slices.

FIELD OF THE INVENTION

The present invention provides a very high resolution single-photonemission computed tomographic (SPECT) imaging tool for brain functionresearch and brain disease diagnosis. It is intended to complement otherfunctional imaging modalities such as positron emission tomography(PET), functional magnetic resonance imaging (fMRI),electroencephalography (EEG) and event-related potential (ERP),magnetoencephalography (MEG), and new, near-infrared optical imaging.

BACKGROUND OF THE INVENTION

In the last quarter century the use of brain imaging for the treatmentand understanding of diseases and genetic flaws has grown dramaticallyfollowing the introduction of Tomographic X-Ray (CT) in 1972 followed in1982 by magnetic resonance in the gene (MRI). The reason for this growthand importance in brain imaging is that neurologists, psychotherapist,and neuro-scientists utilize and attached substantial importance to highresolution, three dimensional anatomical images of the brain. Thedevelopment of functional brain imaging which seeks to map thedistribution of brain activity has closely followed the development ofstructural imaging which maps some physical property of the brain suchas tissue density. While SPECT is playing an important role infunctional brain imaging, it has been limited in many applications byits low spatial resolution. The tiny structures of the brain wherethinking takes place are much smaller than the resolution of the bestSPECT scanners and therefore are not seen. Only in the situations wheregross functional changes or small changes over a large population ofsubjects have occurred is SPECT useful.

U.S. Pat. No. 4,209,700 to Stoddart discloses a first generation nucleartransverse sectional brain function imager. Stoddart discloses animaging apparatus having a transverse radio nuclide scanfield and amethod for using highly focused collimators in an array surrounding thescanfield. This allows the scanner to concentrate its informationgathering capability on a single cross-section of the head as opposed tothe rotating gamma camera whose sensitivity is distributed over theentire volume of the head. In the situations where only part of thebrain is of interest, this is a huge advantage, especially for dynamicstudies where one needs to make rapid repetitive scans of the same area.The scanner is not limited to single sections. By moving the patientthrough the scanner, a stack of sections may be obtained which cover theentire volume of the head.

In general, the typical clinical resolution of the best SPECT rotatinggamma-cameras is about 7 mm. This is inferior to both PET and fMRI whichprovide 5 mm and 3 mm resolution, respectively. The two avenues ofimprovement used to bring rotating gamma-cameras to theirstate-of-the-art are: 1) increasing the number of camera heads (now 3)and 2) modifying the original parallel hole collimator design to thehigher performance mildly converging tapered hole designs' whileincreasing camera area in order to maintain a sufficiently largefield-of-view (FOV). Further improvement is difficult since the camerasof 3-headed systems now totally encircle the patient with little roomleft for more or larger versions.

Collimators are simply blocks of lead with holes drilled through them(or cast with holes in them) to allow gamma rays to pass through whichare traveling in a specific direction. The longer or narrower the holes,the more precise that direction becomes. This is good for geometricalresolution but bad for sensitivity and one needs both. Tapered holes arevastly superior than straight holes in that they provide both bettergeometrical resolution and sensitivity at the same time. While rotationgamma-cameras benefitted from mildly tapered holes, they cannot takeadvantage of highly tapered holes since the resulting FOV would notcover the entire head. The present scanning system overcomes thisproblem by sweeping the narrow FOV.

OBJECT AND SUMMARY OF THE INVENTION

The present invention is a major advance in the resolution of SPECTbrain function imaging, surpassing PET scanners, and equaling fMRI.

The present invention utilizes a collimator with a sharp focus withinthe object, and steeply tapered holes that provide extremely highsensitivity-resolution characteristics. This requires that the detectorbe translated and moved radially-but, with sufficient numbers ofdetectors to provide 360 degree scanfield coverage, no rotationalmovement is necessary. By its nature, namely the constant size andconfiguration of the lead collimator throughout the scanning process,the present scanner has uniform resolution throughout the object volume(spatially invariant point spread function “PSF”) and produces zerospatial distortion. Furthermore, it is immune to various gamma cameraeffects caused by errors in finding exact scintillation locations fromweighted photomultiplier output pulses.

BRIEF DESCRIPTION OF THE DRAWING(S)

FIGS. 1 and 1A show the general arrangement of a particular embodimentof the present invention;

FIG. 2 shows, somewhat schematically, an imager in accordance with thepresent invention;

FIGS. 2A, B and C illustrate a patient in relation to the imager of thepresent invention;

FIGS. 3, 3A and 3B show a detector arrangement, including a highlyfocused collimator, for use in connection with the present invention;

FIG. 4 illustrates schematically an arrangement of highly focusedcollimators in accordance with the present invention and furtherillustrating representative relative movement of the collimators;

FIGS. 4A and 4B illustrate schematically a scanning pattern of highlyfocused collimators in accordance with the present invention;

FIG. 5 shows a preferred scanning pattern in accordance with the presentinvention;

FIGS. 5A and 5B illustrate particular representative portions of thescanning pattern of FIG. 5;

FIG. 6 is a diagram used in connection with a mathematical presentationin the specification;

FIG. 7 schematically represents a general arrangement for the imager ofthe present invention;

FIG. 8A and 8B represents a simplification of the scan pattern from ahorizontal cross section view and a transverse cross section of a sourcebrain view respectively;

FIGS. 9A, 9B and 9C shows a series of 1×2, 2×3 and 3×4 arrays ofscintillation crystals and associated photomultiplier tubes;

FIG. 10 is a theoretical representation of a tapering collimator;

FIG. 11 is a diagrammatic representation of a stacked first and secondcollimators having a focal point at a single point P;

FIGS. 12A and 12B are pictorial representations of a reconstructed anddisplayed image of a brain;

FIGS. 13A and 13B are graphical representations of the improved imagingprocess of the present invention;

FIG. 14 is a block diagram showing a general overview of the systemcomponents;

FIG. 15 is a flow diagram of the reconstruction method;

FIG. 16 is a flow diagram detailing the reconstruction algorithm;

FIG. 17 is a flow diagram of the simulation method used in thereconstruction method and;

FIG. 18 is a flow diagram of a convolution algorithm as used in thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

With reference to FIG. 1, a patient's couch is indicated at 1 which isprovided with controls, not shown, for raising and lowering the couch 1,and for moving the headrest 3, of couch 1, in and out of the opening 5of the gantry indicated at 4. Within gantry 4, as hereinafter more fullydescribed, there is arranged, in a unique and novel manner, a pluralityof scanning detectors, having highly focused collimators, from whichelectrical signals are obtained which are readily processed, e.g. by ageneral purpose computer, and enable a display at console 9 of atransverse section of the brain of a radionuclide administered patient,which display exhibits high sensitivity quantification and spatialresolution. The patients couch 1 is moveable in and out of the opening 5of the gantry 4 to provide for the scanning of a plurality of transversesections.

With reference to FIG. 2, this figure shows at 8 an essentiallyschematic representation of the arrangement of scanning detectors withgantry 4. Each of the detectors indicated at I to XII in FIG. 2 is of atype more fully illustrated in FIGS. 2 and 3A which show a highlyfocused lead collimator at 30, a scintillation crystal at 32, a lightpipe at 34 and a photomultiplier tube at 36. Such an arrangement has thedimensions shown in the drawing when twelve detectors are used tosuitably comprise a collimator made of antimony-bearing lead alloycontaining a 22×26 array of tapered holes of rectangular cross-section.These holes are typically 0.320×0.160 in. On the face of the collimatorthat abuts the scintillation crystal 32, and about 60% of that size atthe opposite face. All of the holes are convergent so that the axesintersect at a focus 6 inches form the collimator. The septa separatingthe holes are approximately 0.0010 inch thick at the crystal face. Atypical design resolution of collimator 30, defined at the full widthbetween two points that give half amplitude for a point source ofradiation is 0.3 inch in the plane of the transverse section and 0.05inch perpendicular to the slice (slice thickness).

The scintillation crystal 32 typically comprises a thallium activatedsodium iodide crystal mounted within a rectangular aluminum box andsealed under a window of ultraviolet transmitting glass. The bottom wallof the aluminum housing is thin, preferably less than 0.02 inches, tominimize absorption and scattering of the incident gamma rays.

A very important feature of the present invention is that the collimatorused is highly focused at a single focal point, i.e. all the holes inthe collimator converge at the focal point so that the collimatorincludes a large solid angle from about 0.05 to 1 steradian, preferablyabout 0.4 steradian, for collecting radiation.

In a configuration such as illustrated schematically in FIG. 2, wheretwelve focused collimators are used, the angle “A” is approximately andas close as practical to 30° (360÷12), e.g. about 24° and the angle “B”shown in FIGS. 2B and 3A is approximately 38.5°. When other than twelvecollimators are used, e.g., 4, 8, 10, the design for angle “A” (±6°) isobtained by dividing the number collimators into 360°. In the presentinvention, the focal length of the collimators (6 inches) is somewhatmore than one-half the diameter of the scan field which surrounds theportion of the patients body which is scanned.

In the present invention, the preferred number of collimators is twelveto obtain high sensitivity and resolution in a short period of time,e.g., about 2 minutes per slice. The preferred range for the number ofcollimators is from 6 to 24 even numbers of collimators. Even umbers ofcollimators are preferred since they can be arranged in pairs with eachcollimator scanning half of the transverse section of the organ therebyminimizing effects of attenuation and scattering. With odd numbers ofcollimators, each collimator preferably scans the entire transversesection of the organ.

Referring again to FIG. 2, detectors I to XII are mechanically mountedand coupled to gantry 4, as hereinafter more fully described, to providefocal point scanning of a transverse section “Z” which is normal thehead-to-toe axis of the patient and indicated schematically in FIG. 2A.With reference to FIG. 2, which shows exemplary distances, the positionof the detectors I-XII can be considered to represent the start (orfinish) of a focal point scan. The alternate pairs of opposed detectorsI-VII, III-IX, V-XI, are shown in what can be called the “full in”position. The other alternate pairs of opposed detectors II-VIII, IV-X,and VI-XII, are in what can be called the “full out” position. Uponcommencement of a scan, each detector I-XII moves in a straight linetangential to the scan filed Z in the same rotational sense (eitherclockwise or counter-clockwise angular rotation abo the “head-to-toe”axis Y of the-patient) the tangential travel of each detector being thesame, a full diameter, or across two adjacent quadrants of scan filed.Upon completion of each tangential travel, the “full in” detectors, I,III, V, VII, IX and XI move away from the axis Y a predeterminedincrement normal to the tangential travel, the “full out” detectors “II,IV etc.” move toward the axis Y by the same increment and the directionof the tangential travel of all detectors is reversed. This coordinatedmovement of the detectors is repeated until the focal point of eachdetector scans at least one half of the area of the scan filed,preferably more than one-half as hereinafter described, at which timethe scanning is completed and the initially “full in” detectors are in“full out” position and vice versa. It is to be noted that the regionscanned by the focal point of each detectors overlaps, by an angularsegment, the focal point scan of the other detectors. In the case oftwelve detectors, there is a 30° segment of overlap of adjacentdetectors and each scanned point in the scan field is scanned by thefocal point of at least six detectors as hereinafter described.

By way of further explanation, FIG. 4 shows schematically, the detectorsI-XII at their respective halfway positions for calibration. At the “½way” position shown in FIG. 4 all of the detectors I-XII are at the samedistance from axis Y and as particularly illustrated for detector I, thefocal point FP_(I) is halfway in the scan field. As the scan iscompleted, detector I moved out and over following the tangential andincremental motion previously described, to the position I′ where thefocal point scan for detector I is completed (Full Scan I).Concurrently, the same relative motion is being experienced by detectorsIII, V, VII, IX and XI. The relative movement of the even numbereddetectors is represented by detector II. As the scan is completed,detector II moves in and over the position II′ where the focal pointscan for detector II is completed (Full Scan II). FIG. 4A illustratesschematically the focal point scan provided by each of the six “outward”moving detector I II, etc. The scan shown is provided, for therespective detector, along the respective radial angle indicated, i.e.a_(I), a_(III)-a_(XI). A similar presentation is shown in FIG. 4B forthe six “inward” going detectors II-XII. As is representativelyillustrated in FIG. 5, any point in the transverse section Z is focalpoint scanned by at least one half of the total detectors, i.e., atleast six in the presently considered embodiment. Because of overlapsthe central region is scanned by up to 12 detectors. This overlap, whichis provided by all twelve detectors in the preferred embodiment of thepresent invention, permits convenient equalization and normalization ofthe detectors. FIG. 5 shows a focal point scan for an “outward” goingdetector e.g. detector I and provides, for a twelve line scan, typicaldimensions for scan line length (8.315 inches) spacing ⅜ inch),resolution elements (128 per line) and the like. As shown in FIG. 5, theexemplary point “R” is “focal point scanned” by the six detectors, I,II, III, IV, V and XII. FIG. 5A is based on FIG. 5 and shows thedetectors which scan two arbitrarily chosen points in the scan fieldwhich are scanned by six detectors; FIG. 5B, also based on FIG. 5, showsthe central region of the scan where scanning by up to twelve detectorsoccurs. The numbers in FIG. 5B show the number of detectors which scanthe indicated region; the same type of information for any point in thescan field can be routinely determined from grids of this type inrelation to the position of the detectors.

In the course of a transverse focal point scan as described above, eachdetector continuously receives the emitted radiation, e.g., gammaphotons appearing within the included angle of the collimator and thisradiation is converted into counts by the associated scintillationcrystal and photomultiplier tube of each detector. Electrical signalsprovided by respective photomultiplier tube can be conventionallyamplified, detected by pulse amplitude discrimination techniques,identified as to spatial orientation in the scan field and, in the formof digital numbers corresponding to counts and detector position,transferred to the memory of a general purpose computer. The storedinformation thus provided is, on account of using highly focusedcollimators in accordance with the present convention, readilyreconstructed to provide a high sensitivity quantification and spatiallocation of the radioactivity in the transverse section which is focalpoint scanned. This is so since focusing collimators inherently sum thecounts from each point, and by focal point scanning in and out as wellas tangentially, the combination of collimators cover (sum)substantially 360° about each point in the transverse scan. The countsthus collected are predominately counts originating at the focal pointsof the collimators but also include (convolved with) some counts from“out of focus points”. These unwanted counts can be removed bydeconvolving the stored information with a filter functionH(r)^(r-k)(K>1) by a relatively simple algorithm such as taking aFourier transform of a ramp in frequency space; for example, asdescribed in “The Fourier Reconstruction of a Head Section”-L. A. Shepp,B. F. Logan “IEEE Transactions on Nuclear Science” vol. NS-21, June1974. The resulting reconstructed data is then available for displayshowing quantified and spatially oriented radioactivity. Other knowntechniques can also be used to remove the unwanted counts.

The concept of using highly focused collimators for this purpose isbased on the recognition that the Radon equation, can be put in a formthat demonstrates that reconstruction using the counts summed(collected) over large angle sis possible.

With reference to FIG. 6

Radon:${G\left( {R,B} \right)} = {\frac{1}{2\pi^{2}}{\int_{- \frac{\pi}{2}}^{+ \frac{\pi}{2}}{\int_{- \infty}^{\infty}{\frac{\partial{F(A)}}{\partial P}\frac{1}{{R\quad{{SIN}\left( {B - A} \right)}} - p}{\mathbb{d}P}{\mathbb{d}A}}}}}$$\quad{\frac{1}{2\pi^{2}}{\int_{o}^{\pi}{{\mathbb{d}A}{\int_{\infty}^{\infty}{\frac{\mathbb{d}{F\left( {P,A} \right)}}{\mathbb{d}P}\frac{1}{{R\quad{SIN}\quad\left( {B - A} \right)} - P}{\mathbb{d}P}}}}}}$

To reconstruct a point at the origin:${G(o)} = {{- \frac{1}{2\pi^{2}}}{\int_{o}^{\pi}{{\mathbb{d}A}{\int_{- \infty}^{\infty}\frac{\mathbb{d}{F\left( {P,A} \right)}}{P}}}}}$

LET dA=Δ, Am=mΔA M=number of projections (π/ΔA).

Replacing Derivative by Difference,${G(o)} = {\frac{\Delta\quad A}{2\pi^{2}}{\sum\limits_{m = 1}^{M}{\sum\limits_{n = 1}^{N}\frac{{F\left\lbrack {{\left( {n + 1} \right)D},{m\quad\Delta\quad A}} \right\rbrack} - {F\left\lbrack {{nD},{m\quad\Delta\quad A}} \right\rbrack}}{\left( \frac{{nD} + {\left( {n = 1} \right)D}}{2} \right)}}}}$${{SINCE}\frac{\Delta\quad A}{\pi}{\sum\limits_{m = 1}^{M}{F\left( {m\quad\Delta\quad A} \right)}}} = {{\overset{\_}{F}{()}}\quad{The}\quad{average}\quad{of}\quad{F{()}}\quad{over}\quad{all}\quad{angles}}$${{AND}\frac{{nD} + {\left( {n + 1} \right)D}}{2}} = {\frac{D}{2}\left( {{2n} + 1} \right)}$${G(o)} = {{{{- \frac{1}{2\pi}} \cdot \frac{2}{D}}{\sum\limits_{n = {- N}}^{N}\frac{\overset{\_}{F}\left\lbrack {\left( {n + {1D}} \right\rbrack - {\overset{\_}{F}({nD})}} \right.}{{2n} + 1}}} - {\frac{1}{D\quad\pi}\begin{Bmatrix}{\frac{{\overset{\_}{F}(D)} - {\overset{\_}{F}(o)}}{1} +} & {\frac{{\overset{\_}{F}\left( {2D} \right)} - {F(D)}}{3} +} & \frac{\overset{\_}{F}\left( {{o\quad 0} - {F\left( {- D} \right)} + \ldots} \right.}{1} \\\left( {n = o} \right) & \left( {n = 1} \right) & {\left( {n = {- 1}} \right)\left( {n = 2} \right)\left( {n = {- 2}} \right)}\end{Bmatrix}}}$$\frac{1}{D\quad\pi}\left\{ {{\overset{\_}{F}(o)} + {\frac{1}{3}\left\lbrack {{\overset{\_}{F}(D)} + {\overset{\_}{F}\left( {- D} \right)}} \right\rbrack} + {\frac{1}{15}\left\lbrack {{\overset{\_}{F}\left( {2D} \right)} + {\overset{\_}{F}\left( {{- 2}D} \right)}} \right\rbrack} + \ldots} \right\}$${G(o)} = {\frac{4}{D\quad\pi}\left\{ {\frac{\overset{\_}{F}(o)}{2} - {\sum\limits_{n = 1}^{N}\frac{\overset{\_}{F}({nD})}{\left( {{4n^{2}} - 1} \right)}}} \right\}}$

In the final equation about

(o),

(nD) are directly measured by the collimators and associated detectors.

With reference to FIG. 7, and the previous description, each focal pointscan line of each detector I-XII, is divided uniformly into 128 discreteresolution elements, the location of which is the scan field is derivedroutinely from the mechanism of the gantry scan drive hereinafter morefully described. As a detector passes through the resolution elements ofa scan line and uniformly samples the resolution elements, accumulator810 accumulates counts from the detector photomultipliers for the timeof detector travel through each resolution element. For example, for atypical resolution element travel time of 150 milliseconds, theaccumulator will receive the counts developed by the detectorphotomultiplier during 4.8 μ second intervals which have an acceptablepulse amplitude as established by a pulse amplitude discrimator circuitin combination with an associated detector. When the counts for a givenresolution element have been received by the accumulator 810, this datais transferred to general purpose computer 840 for storage at an addresscorresponding to the spatial location, i.e. a grid is established inwhich, for each resolution element in the gird, the corresponding countdata representing a quantification of collected counts is stored.

The stored data is then processed by an algorithm, to be discussed infurther detail below.

FIGS. 8A and 8B detail the relative positioning and components of justtwo detectors 400 and 403 which make up the 12 detector array in thetwelve camera scanner of the present invention, Each detector consistsof a photomultiplier tube (PMT) 407 optically coupled to an 8×5×1 inchNal scintillating crystal 409 by means of an integrating sphere 405. Thecrystal 409 is, in turn, attached to the output of a highly focusinglead collimator 411.

FIG. 8A is a view looking down on the 203 mm diameter field of view disk413 in the transaxial plane, while FIG. 8B is looking at the transaxialplane edge-on. The collimator 411 subtends an angle of about 28° in thetransaxial plane as seen in FIG. 15A and 42° in the perpendicular planeas seen in FIG. 8B.

Detector 400 is moved in such a way that its point focus scans theentire near half of the slice in the pattern shown, moving continuouslyin the x1 direction and making a desired number of equal steps in the y1direction. The x1 data is accumulated into either 64 or 128 bins. Forexample, as. As detector 400 makes one full sweep along x1, the numberof events detected by PMT 407 is counted and stored (binned) 128 timesover 128 equal length intervals. Bins With a large number of countscorrespond to detector positions where the detector PSF overlapped areasof high activity.

Detector 403 is shown just 30° from detector 400 and samples the half ofthe transaxial slice nearest it in its own x2, y2 coordinates which arerotated 30° from x1, y1. In order to avoid collision, the even numbereddetectors step in the radially opposite direction from the adjustmentodd numbered detectors.

In FIG. 8A they are shown in the mid y-step passing position. Since the12 detectors together collect data over 336° (12×28), ray angles in thetransaxial slice are adequately sampled and no circumferential rotationis necessary. The bed is advanced in the axial (z) direction to enablethe collimators to scan the next slice.

In order to further improve the resolution of the gamma cameras thereare a number of further embodiments provided below which utilize notonly an improved gamma camera apparatus to provide a more precisephysical collection of data from the emitting source but also a numberof unique application specific algorithms embodied in software formanipulating the acquired data to obtain the most accuratereconstruction and resolved image possible.

Each detector in the known HMX has only one photomultiplier tube. Theoutput of the detector is the sum of all photon detections within itscollimator's solid angle. One issue solved by the present invention is,the possible improvement if each detector, like gamma cameras, wereposition-sensitive and able to keep track of the ray along which eachcount occurred.

The solution described below is that the main effect of making thedetectors position sensitive is to improve the signal-to-noise ratio.This, in turn, improves the fidelity of the reconstruction (whichamplifies noise) and, therefore, ultimately the resolution of thereconstructed images. Image resolution depends on the number andarrangement of detectors, an improvement in system performance isachieved by replacing the single-detector collimators of the HMX imagerwith detector arrays to be described below.

As seen in FIG. 9A, the single 8×5×1 inch Nal crystal of each scanningdetector is replaced with two, 4×5×1 inch crystals, c1 and c2, each withits own photomultiplier (PMT). The addition of two crystals andassociated photomultipliers improves the signal-to-noise ratio for eachscanning detector.

Each detector's PSF spans a rather large (28°×42°) three dimensionalbowtie-shaped volume within the FOV. When a gamma-ray is detected, we donot know where within that volume the gamma-ray originated, only theprobability distribution of its point-of-origin as given by thenormalized PSF. Clearly, if the PSF could be made smaller, the datawould provide better locational information. To achieve this, the firstembodiment is to replace the single 8×5×1 inches Nal crystal of eachdetector with two 4×5×1 inches crystals, labeled c1 and c2 in FIG. 9A,and provide each with its own photomultiplier. This divides the PSF inhalf and increases the number of data values by a factor of two. Now,when a gamma-ray is detected, we will know from which half of thesingle-detector PSF it originated.

Consider a single conical hole bored into a block of lead Pb ofthickness L as shown in FIG. 10, tapered at an angle g and directedalong z. The origin O of the coordinate system is taken to be the apexof the cone. Clearly the projection of the circular entrance aperture501 onto the exit plane 503 as seen from the origin O coincides exactlywith the circular exit aperture. All photons entering from below exitthrough the top. For an off-axis point OA on the focal plane theentrance aperture projects on to the exit plane again as a circle of thesame radius as before but displaced by an amount determined by thedistance of the point form the origin scaled by L/F. Only those photonswhich intersect the overlapping area of the two circles will get through(why is this important?). The solid angle associated with this area is,for small g,$\left. {{{\Omega\left( {x,y,0} \right)} = {\frac{1}{\left( {L + F} \right)^{2}}{\int_{exit}{\int_{plane}{{\mathbb{d}x^{\prime}}{\mathbb{d}y^{\prime}}{{cir}\left( {\frac{x^{\prime}}{R^{\prime}}\frac{y^{\prime}}{R}} \right)}{circ}\frac{x^{\prime} + {\left( {L/F} \right)x}}{R}}}}}},\frac{y^{\prime} + \left( {L/F} \right)}{R}} \right)$where the radius R appearing in the circ functions isR=(L+F)γ

On planes other than the focal plane, the magnification factor L/F andthe radius R in the argument of the second circ function need to bemodified. The effect of this is to broaden W(x,y,z) for z<0 (far field)and narrow it for z>0 (near field). However, by conservation fo photons,the integrated solid angle on any plane remains the same. To simplifyour analysis, we will assume that W(x,y,z) is independent of z and isgiven by the expression for W(x,y,0) above. This is not unreasonablesince in practice as much activity is scanned by the near field as bythe far field. In any case, the exact form of W(x,y) is not important tothe purpose fo this section. What is important is the linear dependenceof the width W(x,y) on Y.

By superposition, the total clear solid angle through a multi-holecollimator as seen by an emitter at r is given by the sum over holes.${\Omega(r)} = {\sum\limits_{i}{\Omega_{i}(r)}}$

If the emitter is producing n photons per unit time, the means countrate will be n W(r)4p. When a density of emitters r(r) is scanned bysuch a collimator, the expected number of observed photons per unit scanvolume is given by the convolution.${\iota(r)} = {\int_{emitters}{{\mathbb{d}^{3}{r^{\prime}\left( \frac{T}{V} \right)}}\frac{\Omega\left( {r - r^{\prime}} \right)}{4\pi}{{vp}\left( r^{\prime} \right)}}}$where T/V is the scan time per unit volume, In k-space, this becomes${\iota(k)} = {\left( \frac{T}{V} \right)\frac{\Omega(k)}{4\pi}{{vp}(k)}}$where m(k), W(k) and r(k) are the Fourier Transforms of m(r), W(r) andr(r). Note that m(k) is dimensionless and is equal the total number ofexpected counts at the spatial frequency k.

We will now evaluate W(k) by performing the sum over holes${\Omega(k)} = {\sum\limits_{i}{\Omega_{i}(k)}}$

For our single conical hole directed along z as previously described, wefind with the help of the convolution theorem that in cylindricalcoordinates${\Omega\left( {k,\phi,\zeta} \right)} = {\frac{\left( {\pi\quad R^{2}} \right)^{2}}{\left( {F + L} \right)^{2}}{{Airy}\left( {\frac{F\left( {F + L} \right)}{L}\gamma\quad k} \right)}2\pi\quad{\delta(\zeta)}}$where d is the Dirac delta function and Airy(x)=(2J₁(x)/x)² in which J₁is the first order Bessel function. For a hole directed along anarbitrary direction {circumflex over (η)} we have merely to rotate theabove expression by replacing d(x) with δ({circumflex over (η)}·k) andinterpret k as the radial coordinate in a spherical system. This is animportant result. It says that the spatial frequency response of acollimator consisting of a number of holes all focused on a single pointmay be constructed by the superposition of a “bundle” of planes whosenormals point in the directions of the holes.

To carry this out, let

{circumflex over (η)}=(sin θ′cos φ′,sin θ′sin φ′,cos θ′) and k=k(sinθcos φ, sin θsin φ, cos θ)

thenδ({circumflex over (η)}·k)=δ(sin θsin θ′cos (φ−φ′)+cos θcos θ′)/k$\frac{{\delta\left( {\phi - \phi^{\prime} - \phi_{r}} \right)} + {\delta\left( {\phi - \phi^{\prime} + \phi_{r}} \right)}}{k\sqrt{{\sin^{2}\theta} + {\cos^{2}\theta^{\prime}}}}$where ±φ_(r) are the values of φ−φ′ for which sinθ sinθ′ cos (φ−φ′)+cosθcosθ′ vanishes. Note that for some combinations of θ and θ′ no rootsexist. To simplify the calculation, we will only consider evaluatingW(k) on the transaxial plane θ=π/2 an the axial line θ=0.

The HMX scanner uses 12 collimators consisting of point focused conicalholes bounded in angle by(π/6)j-π/12≦φ′_(j)≦(π/6)j+π/12 and (π/6)j-π/12≦φ′_(j)≦(π/6)_(j)+π/12where α=24° and j indexes the collimators. Changing the sum over holesto an integral over collimator solid angle yields${\Omega\quad(k)} = {\frac{\left( {\pi\quad R^{2}} \right)^{2}}{\left( {F + L} \right)^{2}}{Airy}\quad\left( {\frac{F\quad\left( {F + L} \right)}{L}\gamma\quad k} \right)\quad 2\quad\pi}$${d\quad\theta^{\prime}\sin\quad\theta^{\prime}{\int{{\mathbb{d}{\theta^{\prime}\left( \frac{\mathbb{d}n}{\mathbb{d}\Omega} \right)}}\frac{\begin{matrix}{{\delta\quad\left( {\phi - \phi^{\prime} - \phi_{r}} \right)} +} \\{{\,^{\frac{\pi}{2}}\delta}\quad\left( {\phi - \phi^{\prime} + \phi_{r}} \right)}\end{matrix}}{k\sqrt{{\sin^{2}\theta} + {\cos^{2}\theta^{\prime}}}}}}} + {\alpha\frac{\pi}{2}} - \alpha$where dn/dΩ is the number of holes per unit solid angle. For a maximallybored collimator this is the reciprocal of the solid angle per hole1/πλ². On the transaxial plane the square root in the denominatorbecomes sinθ′ and φ_(r)=π/2. The only region of non-vanishing Ω are the30° wedges ±90° from the orientation of the collimator${\text{?} + \frac{\pi}{2} - \frac{\pi}{12}} \leq \phi \leq {\phi^{\prime} + \frac{\pi}{2} + {\frac{\pi}{12}{and}\quad\phi^{\prime}} - \frac{\pi}{2} - \frac{\pi}{12}} \leq \phi \leq {\phi^{\prime} - \frac{\pi}{2} + \frac{\pi}{12}}$?indicates text missing or illegible when filedon which${\Omega\quad(k)} = {\frac{\left( {\pi\quad R^{2}} \right)^{2}}{\left( {F + L} \right)^{2}}{Airy}\quad\left( {\frac{F\quad\left( {F + L} \right)}{L}\gamma\quad k} \right)\frac{4\alpha}{\gamma^{2}k}}$

On the axial line we find${\Omega\quad(k)} = {\frac{\left( {\pi\quad R^{2}} \right)^{2}}{\left( {F + L} \right)^{2}}{Airy}\quad\left( {\frac{F\quad\left( {F + L} \right)}{L}\gamma\quad k} \right)\frac{\pi/12}{\gamma^{2}k}}$for every detector with all contribution due to the equatorial belt ofholes at θ′=π/2.

The ability to resolve a feature in the reconstructed image isdetermined by the largest value of k for which the signal power of thefeature remains above the noise power. It is easy to show that noisepower in k-space for a given detector is independent of k (white) and,by the nature of Poisson statistics, is equal to the total number ofcounts N accumulated by the detector over the whole scan.

Two distinct situations are encountered in practice: the imaging ofblood flow agents and the imaging of blood flow agents and the imagingof site specific agents. Blood flow agents are taken up globallyproducing a large noise level which limits the detectability oflow-level localized features. Site-specific agents do not produce muchnoise power but required high bandwidth to resolve. To see whatimprovements can be made in these situations, we set signal power|μ(k)|² to N where p|(k)|² is the power spectrum of the feature to beresolved${{\text{?}(k)}❘^{2}} = {{\left( \frac{T}{V} \right)^{2}\left( \frac{\Omega(k)}{4\pi} \right)^{2}v^{2}{{p(k)}}^{2}} = N}$?indicates text missing or illegible when filedand apply some simple scaling arguments.

According to the expressions for Ω(k) on the previous page, we see thatsignal power depends on k through the two factors, 1/k² andAiry²((F(F+L)/L)γk).

For small k, the first factor governs signal power whereas for kapproaching the geometrical limit, the second factor dominates.Generally speaking, in the case of imaging blood-flow agents, we areoften bandlimited by the 1/k² factor. In this situation, if the aboveequation is balanced at a given value of k then decreasing N to say N′will move the crossover point from k to √(N′IN)γ since the signal powergoes as γ⁴ whereas the nosie power is proportional to γ². According tothe argument of the Airy function, this provides an equal measure ofincreased geometric resolution.

By placing two detectors side-by-side behind each of the twelve HMX'scollimators, will effectively create 24 detectors each spanning a unique15° of asimuthal angle and hence sampling a unique 15° of azimuthalangle in k-space. There will be no loss in signal power, just a cleandivision between which detector samples which angles. Because the totalcounts in these smaller detectors is half previous values, the benefitsdescribed above are achieved. In going to a 3×2 array of detectors, wecreate the same situation regarding the sampling of the axial directionand will be able to take advantage of the 3 times reduction in noisepower. Other directions in k-space should benefit equally well. Largerarrays will provide greater benefit but may ultimately be limited byscattering and the breakdown in the assumption that each hole provides aperfectly thin plane of sensitivity.

In a still further embodiment, not shown, the single Nal crystal may bedivided into three parts, each section measuring 8/3×5×1 inches andhaving an individual photomultiplier tube coupled to it.

Using a plurality of photomultipliers, the detector may send theindividual signals produced by each of the photomultipliers on to thecomputer for treatment as separate data or conversely it may sum thesignals so that they appear to the computer as data from a standardlarge single detector.

Returning now to FIGS. 9B and 9C, a still further embodiment of thedetector consists of a 2×3 array of six individual Nal detectorassemblies c1-c6, including photomultiplier tubes. Each crystal is 68 mmin the axial direction and 63 mm in the transverse direction. Anotherembodiment shown in FIG. 16C utilizes a 3×4 array, each crystal, c1-c12,being 51 mm in the radial direction and 42 mm in the axial direction.The crystals of the arrays are approximately 19 mm thick, compared tothe known crystals being about 25.4 mm thick. These arrays are currentlysized to fit with the current 127×203 mm (5×8 in) envelop of thepresently designed machines, although it is to be appreciated thatdifferent size crystals could be incorporated with machines havingdifferent size envelopes. The important result of the arrayed crystalsis the improved energy resolution obtained for data generation.

Larger arrays are possible, however eventually the information providedby one array element will become redundant with its neighboringelements. From a practical point of view, the number of usable elementsis limited by cost and the ability to handle the increased data ratesand processing load.

A variation of this scheme is to leave the 8×5×1 inch Nal crystal in onepiece and look at the signal crystal with an array of photomultipliersto detect the scintillation light rather than a single detector. Bycomparing the outputs of each photomultiplier, the collimator hole inwhich the interdependence of slice data is due mostly to the axialextent of the PSF and, to a lesser extent, axial correlations in thedistribution of radioactivity in the head. The new algorithm, to bediscussed in further detail below, obtains the distribution ofradioactivity which is most probable given the data and assumed priorinformation on the statistics of that distribution. This solution isknown as a maximum a-posteriori (MAP) reconstruction. The previousreconstruction used a filter and back project technique which could notmodel the counts as Poisson distributed random variables is correct butinstead modeled them as Gaussian distributed with zero mean and astationary variance.

In a yet further embodiment, in combination with the above describedsingle or multiple Nal crystals, the system resolution can be furtherimproved by replacing the present 800-hole collimator with a 1200-holecollimator. Manufacturing tolerances may impose a physical limitation onhow small each rectangular hole in the collimator can be made, however,another alternative is to leave the hole size constant and make thecollimator longer.

Another embodiment combines (stacks) collimators in series as seenschematically in FIG. 11. Each collimator would have the same focalpoint P in space.

Given the above described improvements in the acquisition of accuratedata from the emitting source, the manipulation of this data to accountfor error, absorption and other interference in the physical datacollection by the following method of reconstruction will now bedescribed.

In order to provide a usable, viewable 2 dimensional or 3 dimensionalimage accurately reflecting the scanned section of the source, namely abody organ, it is necessary to provide a method for accuratelyreconstructing the accumulated digital data stored in the host computerinto a viewable image. As is known, the emitted gamma rays from thesource, for example the brain, induce a gamma ray scintillation at theNal crystal causing the release of photons which are “counted” by thephotomultiplier tube. The digital signals of the “count” are then storedin the host computer.

It is important to reconstruct as accurately as possible an imageoptimally reflecting the true emission of the energetic gamma rays fromthe source, therefore the error inherent in the collection of the countmust be eliminated to the extent possible. Because of the highly uniquescanning motion designed to cause the gamma lens foci to uniformlysample the head as is described above, the optimum reconstruction ofimages from the data collected requires not only an accurate actual scanof the source but a specific simulation of this unique scanning motionfor error elimination purposes to be described in further detail below.

Turning now to FIGS. 12A, and 12B, FIG. 12A shows a transaxial brainimage using the below described 3-dimensional reconstruction. FIG. 12Bis an image of a Data Spectrum phantom using the standard 2Dreconstruction. The last pie section to be clearly resolved consists ofan array of 6.4 mm cylinders. The fainter spots located midway betweenthe pie sections are due to some radioactivity leakage along the sixthreaded rods holding the phantom together.

Over the years scans on many animals were made with the HMX using βCITas the injected receptor agent to image the functioning of the caudatenucleus. Old “raw” scan data from the African green monkey model wasutilized to perform a new, fully 3-dimensional reconstruction.

Observing FIGS. 13A and 13B, a profile through the radioactive marker onthe nose is shown at FIG. 19A and a horizontal profile through the headof the caudate nuclei at FIG. 13B. Not only are the left and rightcaudate completely separated in this small animal but the putamen isresolved from the caudate.

Therefore, at least in the case of receptor imaging with its relativelyhigh image contrast, the resolution of the HMX using the new fully 3Dreconstruction is now 3-4 mm. And more preferably a resolution of 2-3 mmis obtainable by using position sensitive detectors discussed herein.

As shown in FIG. 14, the system consists of two parts: (1) the hostcomputer 700 and (2) the scanner 703, and its associated detectors andcollimators as previously discussed. The scanner 703 also includes itsown microprocessors and code which control the radial movement of andrelative timing between the detectors, performs data acquisition via theabove discussed multiple arrays of photomultiplier tubes, and transmitsthe data via serial cable 705 to the host computer 700. Certain physicalattributes of the scanner 703 are difficult to readily improve upon dueto manufacturing and practicality purposes. Some of these attributeswhich improve the data acquisition and the image reconstruction, can,however be enhanced utilizing the following methods of reconstruction asimplemented for example by a computer program on the host computer 700and described in further detail below.

Turning now to FIG. 15 the host computer 700 initiates a scan by sendingcertain setup parameters at step 710 (for example, the number of slices)to the scanner 703 and instructing the scanner to start at step 711.During the scan, acquired data is sent to the host computer in acontinuous stream and compiled at step 713 on its hard disk. Theoperator may instruct the computer to perform a 2-dimensional,slice-by-slice reconstruction at step 715 while the scan is taking placefor the purpose of visually monitoring at step 717 the progress of thescan on the display device 707. Upon completion of acquiring a completedata set for each slice and reconstructing this data into a completevisually observable 2 dimensional slice at step 718, a full3-dimensional reconstruction is performed at step 719 combining theindividual slices into a 3 dimensional model which is visually andstatistically superior in all aspects, to the 2D reconstruction.

Reconstruction

The purpose of the reconstruction, whether 2-dimensional or3-dimensional, is to determine, given the acquired data, the most likelythree dimensional distribution of radioactivity concentration present inthe head at the time of scanning. Observing FIG. 16, the maximuma-posterior (MAP) algorithm described is incorporated in both the 2D and3D reconstructions and is uniquely applicable to the above describedsystem. This algorithm involves an iterative process, which at eachiteration, “moves” the reconstructing distribution of radioactivity froman initial starting point to the final solution. The direction of themove at step n is determined from a comparison of a computer simulatedscan of the solution at step n with the actual scan data. The stepsinvolved are as follows:

-   1. Load scan data into memory at step 730.-   2. Initiate the solution to zero at step 731, i.e. guess the    distribution of radioactivity in the head (an initial guess may    start such a distribution at zero).-   3. Perform a simulated scan of that distribution at step 733.-   4. Compare, at step 735, the simulated scan data collected at step    733 with the real data from the actual scan data and modify the    distribution of radioactivity at step 739, so that on the next pass,    the simulated scan data will better match the real data. (Again, how    the correction is made is specific to our scanner although the math    one goes through to determine this for any scanner is well known).-   5. Determine at step 741 if the solution has changed from the last    iteration, i.e. whether actual scan data and simulated scan data    from step 733 agree within the known statistical noise of the real    data, if yes, then the reconstruction is complete, if no then, steps    735-741 are reiterated until the simulated data and real data agree    to within the known statistical noise of the real data.    Scan Simulation

The goal of the simulation is to model as accurately as possible thepropagation of gamma-rays through the tissues of the head a well as theefficiencies, PSFs and motions of the detectors. Clearly, the better thesimulation, the better will be the agreement between the reconstructedsource distribution and the true source distribution when the simulateddata converges to the real data.

FIG. 17, outlines the simulation procedure. The PSF is generated at step750 at the start of each reconstruction, computing, for every sourcelocation in the field-of-view, the total solid angle of acceptanceallowed by the collimator. This is a straight forward geometry problem,involving the projection of the rectangular holes on the entrance planeof the collimator onto the collimator's exit plane, taking theintersection of the projected rectangular exit-plane holes, multiplyingby a cosine/r² factor and summing over all holes. As this is well knownin the art no further discussion is provided herein.

As described earlier, in the actual data collection process there are 12detectors whose foci simultaneously raster scan the head along threeorthogonal axes. Mathematically, scanning involves the convolution ofthe detector PSFs with the distribution of radioactivity. This isimplemented on the computer using the Fast Fourier Transform (FFT)method. By utilizing both real and imaginary components of the FTarrays, we perform two fo the 12 convolutions with each FFT pairrequiring six FFT pairs all together to complete the 12 convolutions.

Before a convolution is performed, an attenuation map 751 is applied tothe source on a point by point basis to simulate the loss of gamma raysdue to absorption in the head as they make their way toward thedetector. The twelve 3D attenuation maps are pre-computed at step 753 atthe start of a reconstruction using a set of ellipses in step 755, oneper slice, which describe the boundary between head and air and assumingabsorption is constant within the head and zero outside. For each celllocation within a slice and for each detector, attenuation is obtainedby averaging exp(−μs) over the detector's 30° angular field-of-viewwhere s is the distance a gamma ray traverses through the region insidethe slice's ellipse on it way to the detector and μ is the tissueattenuation coefficient. Ellipses are computed from a prior 2Dreconstructions at step 757 and are user adjustable in the event thecomputed ellipses are not deemed satisfactory.

A better strategy for simulating absorption is to acquire two sets ofdata during the actual scan where the second set contains only counts ofscattered gamma rays and use a reconstruction of that data to set thedistribution of absorbers in the simulation assuming equivalence ofscatterers and absorbers.

Turning now to FIG. 18, the convolution algorithm is:FOR i=1 TO6

-   -   1. At step 760 apply the attenuation map corresponding to        detector i to source.    -   2. At step 761 rotate the attenuated source by −30i degrees.    -   3. At step 763 sub-sample the rotated, attenuated source along        the longitudinal direction of the collimator by a factor of 4        and at step 764 put into the real part of a 3D complex array.        (Sub sampling is not required but speeds things up by a factor        of 4 and still maintains Nyquist sampling rates).    -   4. Apply the attenuation map for detector i+6 to source at step        765.    -   5. Rotate the attenuated source by −30i+180 degrees at step 767.    -   6. At step 769 sub-sample the rotated, attenuated source along        the longitudinal direction fo the collimator by a factor of 4        and put into the imaginary part of the same 3D complex array.    -   7. At step 770 perform a 3D Fast Fourier Transform (FFT) on the        complex array.    -   8. At step 771 multiply by the PSF (This is pre-computed at the        start of the reconstruction and is referred to as the modulation        transfer function (MTF).    -   9. At step 773 Inverse FFT.    -   10. Extract real and imaginary parts and set aside at step 775.        LOOP.

The next step is to apply any known systematic errors inherent in theactual scan to the simulated scan. Currently we consider errors in thelocations of the detectors and variation in the efficiencies of thedetectors. These are determined from calibration protocols typicallydone once a day. Offsets are determined form a scan of a line ofactivity placed on axis and in the center of the scanner.

Efficiencies are determined from a scan of a large uniform “flood”source which fills the field-of-view of the scanner.

Source Correction

After adjusting our 12 sets of 3D simulated scans to correspond as bestwe can to actual data, we subtract one from the other. What remains iswhat we would like to get rid of in the next iteration of thereconstruction. To convert this residual error into a source correction,we perform the steps 1 the 10 steps listed above but in reverse orderusing the complex conjugate of the MTF, over-sampling instead ofsub-sampling and counter rotations. The 12 distributions generated inthis manner are summed to form a single 3D distribution whose elementshave a one-to-one correspondence with the elements of the source.

Additional information regarding the source distribution is nowincorporated into the correction. First, we compute the Laplacian of thesource by subtracting from each source element a weighted average of its26 nearest neighbors, scale this by a user selectable amount, thensubtract this 3D distribution from the source correction computed above.The purpose of this is to incorporate into the final solution a priorknowledge of spatial correlation (smoothness). We also provide foradaptive smoothing such that regions of low activity are smoothed morethan regions of high activity. Furthermore, when the correction isfinally applied, source elements which become negative are set to zeroas negative radioactivity is physically not allowed.

1. A brain function imaging apparatus for scanning, mapping and visuallydisplaying functional brain activity, the brain function imagingprocessor comprising: a gantry supporting a plurality of gamma raydetectors, each of said plurality of detectors having at least aconverging collimator for collecting gamma rays emitted from aradioactive source in the brain, a scintillation crystal is attached toan end of each collimator for converting the emitted gamma rays from thebrain into photons of light and at least a photomultiplier tube iscoupled to each scintillation crystal for producing a count of emittedgamma rays; a data processor for digitally compiling the count of gammaradiation and visually reconstructing a digital image reflecting theemitted gamma radiation on a display device; and wherein each of theplurality of converging collimators is a short focus collimator having afocal point within the scanned radioactive source.
 2. A brain functionimaging apparatus for scanning, mapping and visually displayingfunctional brain activity, the brain function imaging processorcomprising: a gantry supporting a plurality of gamma ray detectors, eachof said plurality of detectors having at least a converging collimatorfor collecting gamma rays emitted from a radioactive source in thebrain, a plurality of scintillation crystals attached to an end of eachcollimator for converting the emitted gamma rays from the brain intophotons of light and at least a photomultiplier tube is coupled to eachof said plurality of scintillation crystals for producing a count ofemitted gamma rays; a data processor for digitally compiling the countof gamma radiation and visually reconstructing a digital imagereflecting the emitted gamma radiation on a display device; and whereineach of the plurality of converging collimators is a short focuscollimator having a focal point within the scanned radioactive source.3. (canceled)
 4. A method of digitally constructing and visuallydisplaying brain function activity comprising the steps of: injecting aradioactive isotope into a source brain to facilitate the emission ofgamma radiation from the source brain; scanning the gamma radiationemitted along a first plane of the brain and storing a respective firstdistribution of collected counts of radioactivity as actual scan data inan electronic storage device; digitally reconstructing a brain functionimage from a comparison between the actual scan data of the brain sourceand a theoretical scan of the brain source; and visually displaying thebrain function image as a representation of brain function activity. 5.The method of digitally constructing and visually displaying brainfunction activity as set forth in claim 4 wherein the digitallyreconstructing step further comprises the steps of estimating a seconddistribution of radioactivity in the source brain and performing asimulated scan of the estimated second distribution to obtain thetheoretical scan.
 6. The method of digitally constructing and visuallydisplaying brain function activity as set forth in claim 5 wherein thestep of the reiterated comparison between theoretical and actual scandata further comprises the steps of comparing the theoretical scan withthe actual scan data and modifying the estimated second distribution toobtain a solution gamma radiation distribution which more closely matchthe actual scan data.
 7. The method of digitally constructing andvisually displaying brain function activity as set forth in claim 6further comprising the step of determining whether the solution comparesto the actual scan data within a desired statistical noise.
 8. Themethod of digitally constructing and visually displaying brain functionactivity as set forth in claim 7 wherein when the solution fails tocompare to the actual scan data within the desired statistical noise,the method further comprises the step of modifying the solution with theactual scan data and obtaining a modified solution for comparison withthe actual scan data.
 9. The method of digitally constructing andvisually displaying brain function activity as set forth in claim 7wherein when the modified solution compares to the actual scan datawithin the desired statistical noise, a final completed visual image isproduced which displays the solution gamma radiation distribution at adesired resolution.
 10. The method of digitally constructing andvisually displaying brain function activity as set forth in claim 9wherein the desired resolution of the solution gamma radiationdistribution from the source brain as displayed is between about 1 mmand 7 mm, and more preferably between about 2 mm and 5 mm and mostpreferably between about 2 mm and 3 mm.
 11. The method of digitallyconstructing and visually displaying brain function activity as setforth in claim 4 further comprising the steps of, before digitallyreconstructing the brain function image, repeating the scanning of thegamma radiation emitted along a second through an n^(th) plane of thebrain and storing the respective second through n^(th) distributions ofcollected counts of radioactivity as actual scan data in the electronicstorage device.
 12. A method of digitally constructing and visuallydisplaying brain function activity using a brain function imagingapparatus for scanning, mapping and visually displaying functional brainactivity, the brain function imaging apparatus comprising a gantrysupporting a plurality of gamma ray detectors, each of said plurality ofdetectors having a converging collimator for collecting gamma raysemitted from a radioactive source in the brain, at least a scintillationcrystal is attached to an end of each collimator for converting theemitted gamma rays from the brain into photons of light and at least aphotomultiplier tube is coupled to each scintillation crystal forproducing a count of emitted gamma rays, a data processor for digitallycompiling the count of gamma radiation and visually reconstructing adigital image reflecting the emitted gamma radiation on a displaydevice, each of the plurality of converging collimators is a short focuscollimator having a focal point within the scanned radioactive source,the method comprising the steps of: injecting a radioactive isotope intoa source brain to facilitate the emission of gamma radiation from thesource brain; scanning the emitted gamma radiation with the plurality ofgamma ray detectors, and storing a first distribution of collectedcounts of radioactivity as actual scan data in the data processor;repeating the scanning of the gamma radiation emitted along asequentially adjacent first through n^(th) plane of the brain andstoring a respective first through n^(th) distributions of collectedcounts of radioactivity as actual scan data in the electronic storagedevice. digitally reconstructing the brain function from a reiteratedcomparison between the actual scan data from the sequentially adjacentfirst through n^(th) plane of the brain source and a theoretical scan ofeach adjacent plane of the brain source; and visually displaying thedigital reconstruction of each adjacent first through n^(th) plane ofthe brain as a 3-dimensional image of the brain function activity on thedisplay device.
 13. The method of digitally constructing and visuallydisplaying brain function activity as set forth in claim 12 wherein thedigitally reconstructing step further comprises the steps of estimatinga second distribution of radioactivity in the source brain andperforming a simulated scan of the estimated second distribution toobtain the theoretical scan.
 14. The method of digitally constructingand visually displaying brain function activity as set forth in claim 13further comprising the steps of comparing the theoretical scan with theactual scan data and modifying the estimated second distribution toobtain a solution which more closely match the actual scan data.
 15. Themethod of digitally constructing and visually displaying brain functionactivity as set forth in claim 14 further comprising the step ofdetermining whether the solution compares to the actual scan data withina desired statistical noise.
 16. The method of digitally constructingand visually displaying brain function activity as set forth in claim 15wherein when the solution fails to compare to the actual scan datawithin the desired statistical noise the method further comprises thestep of modifying the solution with the actual scan data and obtaining amodified solution for comparison with the actual scan data.
 17. Themethod of digitally constructing and visually displaying brain functionactivity as set forth in claim 15 wherein when the modified solutioncompares to the actual scan data within the desired statistical noise, afinal completed output is produced which visually displays the gammaradiation distribution from the source brain on the display device at adesired resolution.
 18. The method of digitally constructing andvisually displaying brain function activity as set forth in claim 12wherein each detector is provided with 3 separate scintillation crystalseach crystal having an associated photomultiplier tube for providingthree channels of input to the data processor from each detector. 19.The method of digitally constructing and visually displaying brainfunction activity as set forth in claim 12 wherein each convergingcollimator of each detector comprises a plurality of stackedcollimators.
 20. A method of digitally constructing and visuallydisplaying brain function activity of a brain source comprising thesteps of: injecting a radioactive isotope into the source brain tofacilitate the emission of gamma radiation from the source brain;scanning the emitted gamma radiation and storing collected counts ofemitted gamma radiation in an electronic storage device; and visuallydisplaying an image of the brain function activity by digitallyreconstructing the image of brain function from a reiterated comparisonbetween collected data from an actual scan data of the brain source anda theoretical scan of the brain source.